Questions: Select the outlier in the data set. 60 53 55 75 68 88 86 73 198 44

Solution Steps

Arrange the given data set in ascending order: \[ 44, 53, 55, 60, 68, 73, 75, 86, 88, 198 \]

1. Find the first quartile (\( Q_1 \)) and the third quartile (\( Q_3 \)):
   • \( Q_1 \) is the median of the first half of the data: \( Q_1 = 55 \).
   • \( Q_3 \) is the median of the second half of the data: \( Q_3 = 86 \).
2. Calculate the IQR: \[ \text{IQR} = Q_3 - Q_1 = 86 - 55 = 31 \]

1. Calculate the lower bound: \[ \text{Lower bound} = Q_1 - 1.5 \times \text{IQR} = 55 - 1.5 \times 31 = 55 - 46.5 = 8.5 \]
2. Calculate the upper bound: \[ \text{Upper bound} = Q_3 + 1.5 \times \text{IQR} = 86 + 1.5 \times 31 = 86 + 46.5 = 132.5 \]
3. Any data point below the lower bound or above the upper bound is considered an outlier. In this case, \( 198 \) is above the upper bound (\( 132.5 \)), so it is an outlier.

Final Answer